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Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.

- Publication
- IEICE TRANSACTIONS on Communications Vol.E104-B No.3 pp.251-261

- Publication Date
- 2021/03/01

- Publicized
- 2020/09/01

- Online ISSN
- 1745-1345

- DOI
- 10.1587/transcom.2020EBP3051

- Type of Manuscript
- PAPER

- Category
- Fundamental Theories for Communications

Yusuke SAKUMOTO

Kwansei Gakuin University

Masaki AIDA

Tokyo Metropolitan University

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Yusuke SAKUMOTO, Masaki AIDA, "Wigner's Semicircle Law of Weighted Random Networks" in IEICE TRANSACTIONS on Communications,
vol. E104-B, no. 3, pp. 251-261, March 2021, doi: 10.1587/transcom.2020EBP3051.

Abstract: Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.

URL: https://global.ieice.org/en_transactions/communications/10.1587/transcom.2020EBP3051/_p

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@ARTICLE{e104-b_3_251,

author={Yusuke SAKUMOTO, Masaki AIDA, },

journal={IEICE TRANSACTIONS on Communications},

title={Wigner's Semicircle Law of Weighted Random Networks},

year={2021},

volume={E104-B},

number={3},

pages={251-261},

abstract={Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.},

keywords={},

doi={10.1587/transcom.2020EBP3051},

ISSN={1745-1345},

month={March},}

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TY - JOUR

TI - Wigner's Semicircle Law of Weighted Random Networks

T2 - IEICE TRANSACTIONS on Communications

SP - 251

EP - 261

AU - Yusuke SAKUMOTO

AU - Masaki AIDA

PY - 2021

DO - 10.1587/transcom.2020EBP3051

JO - IEICE TRANSACTIONS on Communications

SN - 1745-1345

VL - E104-B

IS - 3

JA - IEICE TRANSACTIONS on Communications

Y1 - March 2021

AB - Spectral graph theory provides an algebraic approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the network. However, it is difficult to accurately represent the structures of large-scale and complex networks (e.g., social network) as a matrix. This difficulty can be avoided if there is a universality, such that the eigenvalues are independent of the detailed structure in large-scale and complex network. In this paper, we clarify Wigner's Semicircle Law for weighted networks as such a universality. The law indicates that the eigenvalues of the normalized Laplacian matrix of weighted networks can be calculated from a few network statistics (the average degree, average link weight, and square average link weight) when the weighted networks satisfy a sufficient condition of the node degrees and the link weights.

ER -